Addition and Difference (trigonometric)

Question

Given: cos a = -24/25, sin b = 3/5, a and b are second-quadrant angles: find cos(a - B)

Answer 1

cosa =-24/25, sinb = 3/5, a,b in Q2

cos(a-b) = cosacosb + sinasinb

= (-24/25)(-4/5) + (7/25)(3/5)

= 96/125 + 21/125

= exactly 117/125

= about .936

check the answer:

b = sin^-1(3/5) = sin^-1(.6) = 36.87+90 = 126.87

a = sin^-1(7/25) =sin^-1(.28) =16.26 +90 =106.26

cos(a-b) = cos(126.87-106.26)= cos20.61 = .936

a & b are in Q2, but a-b is in Q1